Yet the mere fact that I am conscious is a greater truth than any of my perception of the "physical" world.

Neither does pure materialism rest on falsifiable beliefs, in that I could claim nothing exists outside my conscious experience.

> Any argument that a "soul" exists or that consciousness does not arise from the physical world (eg our neurons) is literally unfalsifiable.

This is an metaphysical discussion, so falsifiability is kind of irrelevant. All metaphysical positions are ultimately unfalsifiable - including materialism and physicalism just as much as dualism or monism or theism.

It would only be unfalsifiable if the connection was one-way, i.e. our souls receive input from the world but have no effect on the world. We would effectively be passengers in a meat puppet, and any influence we have on that puppet is purely imaginary. Certainly possible, but not usually how it's conceived, and then you have the question of how the meat puppets got the idea of consciousness and souls in the first place.

If souls can influence the world, as is the common belief for souls, then in principle that influence or its absence can be detected.

Argue with someone who gathered evidence scientifically to demonstrate that we really, really don't know what we're talking about when it comes to the human soul:

https://en.wikipedia.org/wiki/Twenty_Cases_Suggestive_of_Rei...

EDIT: Downvote all you want, materialists, but reincarnation is the spanner in the works nobody wants to confront ..